Stokes Darcy耦合问题的新等阶元投影稳定化方法

针对Stokes Darcy耦合问题提出一种新的投影稳定化方法，该方法对整个区域采用统一的等阶有限元空间逼近.相比通常的局部投影稳定化方法，增加了新的投影稳定项以及压力跳跃项，有效地克服了等阶有限元不满足inf sup条件的困难，也保证了该方法不仅对不连续的压力空间适用，且对连续的压力空间亦适用. 最后，证明了该方法的稳定性，并给出了误差估计.

New projection-type stabilization with equal-order elements for coupled Stokes-Darcy flow

A new projection type stabilized formulation for the coupled Stokes Darcy flow is proposed. The method is based on the same equal order mixed finite element space for both regions. Compared with usual local projection stabilization methods, we add a new projection type stabilization term and a pressure jump term, which can effectively bypass the inf sup condition. It also ensures that our technique can be applied to not only discontinous pressure space but also continuous pressure space. At last, the stability of the proposed scheme is proved, and error estimates are obtained.